Reverse Power Rule (Integration)

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What is the Reverse Power Rule in integration?

Back

The Reverse Power Rule states that for any real number n ≠ -1, the integral of x^n is given by: \( \int x^n dx = \frac{x^{n+1}}{n+1} + C \) where C is the constant of integration.

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Front

If f'(x) = 6x, what is f(x)?

Back

Front

Given f(-3) = 20, find the constant C if f(x) = 3x^2 + C.

Back

C = 20 - 27 = -7, so f(x) = 3x^2 - 7.

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Front

What is the constant of integration?

Back

The constant of integration (C) represents an arbitrary constant added to the indefinite integral, accounting for all possible antiderivatives.

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How do you find the definite integral of a function?

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To find the definite integral, evaluate the indefinite integral at the upper limit and subtract the value at the lower limit: \( \int_a^b f(x)dx = F(b) - F(a) \) where F is the antiderivative of f.

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What is the integral of a constant?

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The integral of a constant k is given by: \( \int k \, dx = kx + C \) where C is the constant of integration.

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What is the power rule for differentiation?

Back

The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).